M2399087 Mersenne number exponent details

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is 2 ^2399087 - 1

has 722198 decimal digits

takes 0.162 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	BD5BEBAF5F85A99A	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	24.8448	67.6471%	3000000	100000000	0.8115	7.8465%	25.6564	70.1856%	2.5386%
PrimeNet	2⁵⁹	0.0320	62.7119%	10000	170000	0.0018	2.4795%	0.0338	63.6364%	0.9245%
GPU72	2⁶³	0.6653	65.0794%	10000	140000	0.0017	1.2747%	0.6669	65.5245%	0.4451%
Difference	+5	+24.1796	+2.5677%	+2990000	+99860000	+0.8099	+6.5718%	+24.9894	+4.6611%	+4.6611%

Known prime factors (1 factor, 74.8 bits, 0.00311838% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2399087	33179580451086138126271	23	74.813	6915043191657105 3⁴ × 5 × 17 × 139 × 7225637207	2020-07-28	139	7225637207	2,832.2	38.562	72.024

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-21T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.232%
2010-11-08T22:12:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.203%
2010-11-16T23:08:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.261%
2010-12-23T04:54:00	markr	tiny	90000	1845000		-		-	-	0.018	-	-	2.310%
2014-08-21T02:33:00	Jocelyn Larouche	Manual testing	116754	116754		-		-	-	0.011	-	-	0.894%
2014-11-06T23:05:00	Jocelyn Larouche	Manual testing	143508	143508		-		-	-	0.014	-	-	1.004%
2015-12-18T08:13:12	mikr	MSI	3000000	100000000	12	-		-	-	0.812	-	-	7.847%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.032	-	-
2016-02-23T16:29:13	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.032	-	-
2009-01-15T06:14:00	Sturle Sunde	ghibu.ifi	2⁶⁰	2⁶¹		-	-	0.064	-	-
2012-06-02T14:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.128	-	-
2013-01-23T08:27:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.409	-	-
2015-03-12T10:49:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.818	-	-
2015-03-12T10:49:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.557	-	-
2015-11-05T09:47:19	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.115	-	-
2017-06-27T22:16:40	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.230	-	-
2019-02-25T14:14:31	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	12.46	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.231 GHz-days
Estimated T-Level:	3.500

Digits	B1	Curves	Complete	FacMiss
20	11000	70 / 100	0.700	49.484%
25	50000	70 / 280	0.250	77.845%

New Calculation Method

Total ECM effort:	6.231 GHz-days
Estimated T-Level:	3.500

Digits	B1	Complete	FacMiss
20	11000	2.258	10.455%
25	50000	0.204	81.540%
30	250000	0.013	98.751%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		69	6.142
50000	5000000	33179580451086138126271	1	0.089

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-06-15T00:00:00	ANONYMOUS	v4_computers	BD5BEBAF5F85A99A	0.162
2018-05-18T05:12:52	kkmrkkblmbrbk	old	BD5BEBAF5F85A99A	0.162

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-07-31T10:45:03

Klaus Nordmann

no1

33179580451086138126271

E7172CF173B48404

no

2020-07-31T11:38:28

SRJ2877

Manual testing

33179580451086138126271

E7172CF173B48404

no

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 90000, B2 = 1845000 (P-1 stage 2)

B1 = 143508 (P-1 stage 1)

B1 = 116754 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10¹

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TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-07-31T11:38:28+00:00